where \(\delta =\frac{\pi }{2a}\) , is a scaling factor depending on
the width of the well. This potential models a QHO placed in the
center of the rectangular infinite well [1]}. The potential
\(V(x)\)  (REF ) fulfills two asymptotic requirements: 1)
\(V(x)\rightarrow \frac{1}{2}kx^2\)  when \(a\rightarrow \infty \)  (free
harmonic oscillator limit). 2) \(V(x)\)  at equilibrium position has
the same curvature as a free QHO,
\(\left[\frac{d^2V}{dx^2}\right]_{x=0}=k\) . This model potential belongs
to the exactly solvable trigonometric Pöschl-Teller potentials family [2]}.
Stationary coherent states for special kind of this potential have been
considered [3]}.
